本文采用指数效用最大化的方法研究了期权的动态无差异效用价值过程Ct(H;α).考虑股票价格过程为具有基于随机测度的一般跳的半鞅模型,且期权的无差异效用价值过程的Doob-Meyer分解的鞅部分的GKW(Galtchouk-Kunita-Watanabe)分解满足Ja...本文采用指数效用最大化的方法研究了期权的动态无差异效用价值过程Ct(H;α).考虑股票价格过程为具有基于随机测度的一般跳的半鞅模型,且期权的无差异效用价值过程的Doob-Meyer分解的鞅部分的GKW(Galtchouk-Kunita-Watanabe)分解满足Jacod鞅表示定理.利用无差异效用价值过程在最小熵测度和最优投资策略下为鞅的事实构建了一个倒向随机微分方程.通过概率测度变换将方程的鞅部分和生成元转化为BMO(bounded mean oscillation)鞅,证明了该方程的解的唯一性.并将方程的生成元分成[?A=0]和[?A≠0],证明了最优投资策略存在.从而给出期权无差异效用价值过程的倒向随机微分方程的表达形式.展开更多
This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward gener...This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward generator requires only mild regularity assumptions.The authors showthat the Four Step Scheme introduced by Ma,et al.(1994) is still effective in this case.Namely,the authors show that the adapted solution of the FBSDE exists and is unique over any prescribedtime duration;and the backward components can be determined explicitly by the forward componentvia the classical solution to a system of parabolic integro-partial differential equations.An importantconsequence the authors would like to draw from this fact is that,contrary to the general belief,in aMarkovian set-up the martingale representation theorem is no longer the reason for the well-posednessof the FBSDE,but rather a consequence of the existence of the solution of the decoupling integralpartialdifferential equation.Finally,the authors briefly discuss the possibility of reducing the regularityrequirements of the coefficients by using a scheme proposed by F.Delarue (2002) to the current case.展开更多
文摘本文采用指数效用最大化的方法研究了期权的动态无差异效用价值过程Ct(H;α).考虑股票价格过程为具有基于随机测度的一般跳的半鞅模型,且期权的无差异效用价值过程的Doob-Meyer分解的鞅部分的GKW(Galtchouk-Kunita-Watanabe)分解满足Jacod鞅表示定理.利用无差异效用价值过程在最小熵测度和最优投资策略下为鞅的事实构建了一个倒向随机微分方程.通过概率测度变换将方程的鞅部分和生成元转化为BMO(bounded mean oscillation)鞅,证明了该方程的解的唯一性.并将方程的生成元分成[?A=0]和[?A≠0],证明了最优投资策略存在.从而给出期权无差异效用价值过程的倒向随机微分方程的表达形式.
基金supported by the National Science Foundation under Grant Nos. #DMS 0505472, 0806017,and#DMS 0604309
文摘This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward generator requires only mild regularity assumptions.The authors showthat the Four Step Scheme introduced by Ma,et al.(1994) is still effective in this case.Namely,the authors show that the adapted solution of the FBSDE exists and is unique over any prescribedtime duration;and the backward components can be determined explicitly by the forward componentvia the classical solution to a system of parabolic integro-partial differential equations.An importantconsequence the authors would like to draw from this fact is that,contrary to the general belief,in aMarkovian set-up the martingale representation theorem is no longer the reason for the well-posednessof the FBSDE,but rather a consequence of the existence of the solution of the decoupling integralpartialdifferential equation.Finally,the authors briefly discuss the possibility of reducing the regularityrequirements of the coefficients by using a scheme proposed by F.Delarue (2002) to the current case.
